; Imperative prime sieve in Scheme.

(define (sieve-out pivot number-list)
  (let ((i number-list)
        (result '())
        (result-tail '()))
    (while (not (null? i))
      (if (not (zero? (modulo (car i) pivot)))
        (if (pair? result)
          (begin
            (set-cdr! result-tail (cons (car i) '()))
            (set! result-tail (cdr result-tail)))
          (begin
            (set! result (list (car i)))
            (set! result-tail result))))
      (set! i (cdr i)))
    result))

(define (sieve number-list)
  (let ((i number-list)
        (result '())
        (result-tail '()))
    (while (not (null? i))
      (if (pair? result)
        (begin
          (set-cdr! result-tail (cons (car i) '()))
          (set! result-tail (cdr result-tail)))
        (begin
          (set! result (cons (car i) '()))
          (set! result-tail result)))
      (set! i (sieve-out (car i) i)))
    result))

(define (find-primes-to to)
  (let ((numbers '())
        (i to))
    (while (> i 2)
      (set! numbers (cons i numbers))
      (set! i (1- i)))
    (sieve numbers)))